David Corfield explanation, evidence, cause

What did I see in lenses and modality?

So a lens (in cs) is just an algebra for what I called the possibility monad in my SYCO 1 talk - https://ncatlab.org/davidcorfield/files/ModalBirm.pdf? If so, curious that @_julesh_ , the other invited speaker, told us about these, while I dwelt on coalgebras for the necessity comonad. Dual talks.

Does the lenses literature intersect with that of type refinement: https://ncatlab.org/nlab/show/type+refinement? A refinement is a lift over a morphism in the base, which seems much like what’s happening with a bimorphic lens (S, T) -> (A, B).

S is fibred over A, and T over B, and you want to know where to send an element of S in T, given an element of B.

Perhaps ‘Positive Subtyping’, https://doi.org/10.1006/inco.1996.0031.

Evidence as three part relation, evidence for something in this context.

Chang and Fisher on two kinds of evidence: proposition-proposition, process-trace.

MacIntyre on cause as four place relation, A is cause of B against background C, when otherwise would have happened.

Does this explain difference-making and production?

Jaynes, Probability of A given B in context of background information.

Evidence not reducible to propositions, but to way enquiry is organised.

DTT and conditional probability.

van Fraassen on explanation and contrast.

DTT and questions.